Anti-concentration and honest, adaptive confidence bands

@article{Chernozhukov2013AnticoncentrationAH,
  title={Anti-concentration and honest, adaptive confidence bands},
  author={Victor Chernozhukov and Denis Chetverikov and Kengo Kato},
  journal={arXiv: Statistics Theory},
  year={2013}
}
Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the classical Smirnov-Bickel-Rosenblatt (SBR) condition; see, for example, Gin\'{e} and Nickl [Probab. Theory Related Fields 143 (2009) 569-596]. This condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process (equivalently, for the supremum of a Gaussian process with the same covariance function as that of… 
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